WORK IN PROGRESS
Cell Bio is a discipline in its own right. You can learn lots from an A-Level/College level text book. Most manipulation is done via genetics which is a separate, though related discipline.
However many drugs, hormones and other substances interact with cells and change how they work.
Cell Membrane - this is the 'wall' of the cell, it has various gates which only allow some substances in or out. It has receptors over it which react with hormones or other molecules.
Cytoplasm - the gloop inside the cell. What all the stuff floats around in. Also contains ribosomes which often aren't shown on typical diagrams.
Ribosome - has 2 sub-units which lock together over an RNA strand to enable translation. (https://en.wikipedia.org/wiki/Eukaryotic_ribosome_(80S)
Endoplasmic Reticulum - basically has a load of ribosomes.
Golgi apparatus - coats proteins to leave the cells in a membrane that allows them to travel out of the cell.
Mitochondria - an organelle that has its own type of DNA (inherited from maternal line) and is involved in synthesising ATP which is the fundamental unit of energy for the body.
Nucleus - contains the chromosomes which contain the DNA.